Sources

Game and Story Use

If they own so many skulls, do they also own Baphomet, the idol allegedly worshiped by the Knights Templar? And if so, does Baphomet rule America via its Skull and Bones proxies?

The skulls might be kept for purposes of (literal) necromancy - calling up the spirits of deceased notables for advice and guidance.

More worrying still, the skulls may serve as soul jars and the spirits of the dead may actually be borrowing the bodies of living members - with the body's original inhabitant transferring to the skull for the duration. This might give you a society in which you forfeit freehold of your body during your lifetime in return for indefinite timeshare of the bodies of future members … and outsiders can never be entirely sure who is behind the eyes of any given body.

Perhaps you have to contest ownership of your body with previous members - if you succeed, you become a full member and are admitted to storage upon your death, if you fail your soul is consumed and your body passes to a previous member to live out another life.